C₁₀₉×#2153 #28359407

order	13952
nilpotency class	3
isoclinism	isoclinic class of AGL(1,ℤ/8)
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₀₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₀₉×#2153

Subgroups

	subgroup	G/H
center	C₈×C₁₀₉	C₂×D₄
commutator	C₄	C₂²×C₈×C₁₀₉
Frattini, cosocle	C₂×C₈	C₂³×C₁₀₉
socle	C₂×C₁₀₉	C₂×C₄⋊C₈
prime radical	C₂³×C₁₀₉	M₁₆
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₁₀₉ ◁ C₂²×C₈×C₁₀₉ ◁ G

152 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 141
transitive degree	μ_t(G) = 3488

A minimal faithful permutation representation — 3 generators on 141 points:

(1,2,5,10,6,9,19,24,7,11,20,25,4,17,18,30)(3,12,15,27,16,22,29,31,13,26,28,32,14,8,21,23)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141);(1,3,4,14,7,13,6,16)(2,8,9,12,11,22,17,26)(5,15,18,21,20,28,19,29)(10,23,24,27,25,31,30,32);(3,13)(8,22)(12,26)(14,16)(15,28)(21,29)(23,31)(27,32)

Conjugacy classes & character table

4796 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₀₉×#11989, C₁₀₉×#11990, C₁₀₉×#11991, …
maximal normal subgroup of	C₁₀₉×#11989, C₁₀₉×#11990, C₁₀₉×#11991, …
maximal quotient of	C₁₀₉×#11997, C₁₀₉×#12005, C₁₀₉×#12014, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 885);

C109×#2153 #28359407